A249651 Decimal expansion of Integral_{0..1} Li_2(x)^2 dx, where Li_2 is the dilogarithm function.

6, 0, 7, 7, 1, 2, 3, 3, 7, 9, 4, 3, 0, 1, 5, 4, 6, 4, 2, 4, 6, 2, 2, 6, 2, 6, 2, 0, 1, 5, 0, 6, 9, 4, 1, 5, 4, 3, 9, 0, 3, 2, 4, 0, 8, 0, 2, 1, 2, 2, 4, 8, 6, 6, 5, 6, 7, 2, 3, 7, 8, 5, 8, 5, 0, 2, 9, 3, 3, 7, 7, 6, 5, 1, 5, 7, 6, 8, 0, 0, 7, 9, 7, 9, 1, 9, 2, 7, 9, 4, 1, 7, 7, 3, 9, 1, 3, 4, 9, 8, 8, 9, 6, 7, 1, 7

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's MathWorld, Dilogarithm

Formula

6 - 2*zeta(2) - 4*zeta(3) + zeta(2)^2.

Example

0.607712337943015464246226262015069415439032408...

Mathematica

RealDigits[6 - 2*Zeta[2] - 4*Zeta[3] + Zeta[2]^2, 10, 106] // First
NIntegrate[PolyLog[2, x]^2, {x, 0, 1}, WorkingPrecision->110] (* Vaclav Kotesovec, Nov 03 2014 *)

Prog

(Python)
from mpmath import *
mp.dps=107
f=lambda x: polylog(2, x)**2
I=quad(f, [0, 1])
print([int(n) for n in list(str(I)[2:-1])]) # Indranil Ghosh, Jul 04 2017

Crossrefs

Cf. A002117, A013661, A249649.

Sequence in context: A365163 A195432 A196915 * A021626 A320376 A059956

Adjacent sequences: A249648 A249649 A249650 * A249652 A249653 A249654

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Nov 03 2014

Status

approved